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Re: st: problem with generated regressands and WLS


From   Arka Roy Chaudhuri <gabuisi@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: problem with generated regressands and WLS
Date   Wed, 13 Oct 2010 12:18:09 -0700

I shall repost my earlier mail(using full names for the Greek
characters) as I just learnt that many might not be able to see the
Greek characters.I am extremely sorry for my mistake and the
inconvenience caused.
I wrote:
 Thanks for the response. Sorry for not making my notation clearer- I
had used x for the independent variables in both the first and second
stage.Revising my notation:

 1st stage:
 y = alpha  + beta1x1+ beta2x2 +................. +betanxn+ rho1z1 +  rho2z2 + u

 2nd stage:
  beta= p + deltaq + error

 In the first stage y is the dependent variable and x1...xn, z1,z2 are
 the independent variables, beta1-betan and rho1-rho2 are the parameters.alpha
 and p are the intercepts in the first and  second stage respectively.
 The beta's(beta1.....betan) from the first stage constitute my dependent
 variable in the second stage-since there are n of them I have n
 observations for my dependent variable in the second stage. q is the
 independent variable in the second stage and delta is the parameter
to be estimated. I also
 have n observations  of q.
  Yes I do want to improve efficiency although I am not sure how.
 Should I use the entire variance-covariance matrix of the beta's from the
 first stage as the weighing matrix in the second stage?Or should I
 just use the variance(from the first stage) of the betas as analytic
 weights in the second stage?If I use the second method should not
 non-zero covariances across the observations(beta's) affect my
 results?Also if I am to use the entire variance-covariance matrix as
 the weighing matrix how should I implement it in Stata?Please
 advice.Thanks

Arka

2010/10/12 Arka Roy Chaudhuri <gabuisi@gmail.com>:
> Thanks for the response. Sorry for not making my notation clearer- I
> had used x for the independent variables in both the first and second
> stage.Revising my notation:
> 1st stage:
> y = α + β1x1+ β2x2 +................. +βnxn+ ρ1z1 +  ρ2z2 + u
>
> 2nd stage:
>  β= p + δq + ε
>
> In the first stage y is the dependent variable and x1...xn, z1,z2 are
> the independent variables.α and p are the intercepts in the first and
> second stage respectively.
> The β's(β1, β2,......βn) from the first stage constitute my dependent
> variable in the second stage-since there are n of them I have n
> observations for my dependent variable in the second stage. q is the
> independent variable in the second stage. I also have n observations
> of them.
>  Yes I do want to improve efficiency although I am not sure how.
> Should I use the entire variance-covariance matrix of the β's from the
> first stage as the weighing matrix in the second stage?Or should I
> just use the variance(from the first stage) of the betas as analytic
> weights in the second stage?If I use the second method shouldn't
> non-zero covariances across the observations(β's) affect my
> results?Also if I am to use the entire variance-covariance matrix as
> the weighing matrix how should I implement it in Stata?Please
> advice.Thanks
>
> Arka
>
> 2010/10/12 Austin Nichols <austinnichols@gmail.com>:
>> Arka Roy Chaudhuri <gabuisi@gmail.com>:
>> If you think beta is measured with an independent error, i.e. no
>> endogeneity or other endemic problems, you can ignore the fact that it
>> is generated; measurement error in the depvar is usually not a
>> problem. But perhaps you are looking for improved efficiency, and you
>> want to use the squared SE on beta as a measure of the error
>> variance--but it does not vary by observation--see the manual entry on
>> -vwls- for example.  Is your "second stage" in matrix form using the
>> same y and x and so forth, or have you reused notation?
>>

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